On the representation of measures over bounded lattices
In this paper we investigate measures over bounded lattices, extending and giving a unifying treatment to previous works. In particular, we prove that the measures of an arbitrary bounded lattice can be represented as measures over a suitably chosen Boolean lattice. Using techniques from algebraic g...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/181158 |
| Acceso en línea: | http://hdl.handle.net/11336/181158 |
| Access Level: | acceso abierto |
| Palabra clave: | LATTICES MEASURABILITY MEASURE FUNCTOR REPRESENTABILITY https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | In this paper we investigate measures over bounded lattices, extending and giving a unifying treatment to previous works. In particular, we prove that the measures of an arbitrary bounded lattice can be represented as measures over a suitably chosen Boolean lattice. Using techniques from algebraic geometry, we also prove that given a bounded lattice X there exists a scheme X such that a measure over X is the same as a (scheme-theoretic) measure over X. We also define the measurability of a lattice, and describe measures over finite lattices. |
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